\newproblem{lay:5_1_1}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 5.1.1}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Is $\lambda=2$ an eigenvalue of $\begin{pmatrix}3 & 2 \\ 3 & 8\end{pmatrix}$? Why or why not?
}{
   % Solution
	To check whether $\lambda=2$ is an eigenvalue or not, we test whether it is a solution of the equation
	\begin{center}
		$\left|\begin{pmatrix}3 & 2 \\ 3 & 8\end{pmatrix}-\lambda I\right|=0 \Rightarrow
		\left|\begin{pmatrix}3 & 2 \\ 3 & 8\end{pmatrix}-2 \begin{pmatrix}1 & 0 \\ 0 & 1\end{pmatrix}\right|=0 \Rightarrow
		\left|\begin{array}{cc}1 & 2 \\ 3 & 6\end{array}\right|=0 \Rightarrow 0=0$
	\end{center}
	Since we have got an identity ($0=0$), $\lambda=2$ is a solution of the eigenvalue problem and it is an eigenvalue of the proposed matrix.
}
\useproblem{lay:5_1_1}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
